Problem: $\dfrac{ 3l - 8m }{ -8 } = \dfrac{ 3l + 5n }{ -2 }$ Solve for $l$.
Multiply both sides by the left denominator. $\dfrac{ 3l - 8m }{ -{8} } = \dfrac{ 3l + 5n }{ -2 }$ $-{8} \cdot \dfrac{ 3l - 8m }{ -{8} } = -{8} \cdot \dfrac{ 3l + 5n }{ -2 }$ $3l - 8m = -{8} \cdot \dfrac { 3l + 5n }{ -2 }$ Reduce the right side. $3l - 8m = -{8} \cdot \dfrac{ 3l + 5n }{ -{2} }$ $3l - 8m = {4} \cdot \left( 3l + 5n \right)$ Distribute the right side $3l - 8m = {4} \cdot \left( {3l} + {5n} \right)$ $3l - 8m = {12}l + {20}n$ Combine $l$ terms on the left. ${3l} - 8m = {12l} + 20n$ $-{9l} - 8m = 20n$ Move the $m$ term to the right. $-9l - {8m} = 20n$ $-9l = 20n + {8m}$ Isolate $l$ by dividing both sides by its coefficient. $-{9}l = 20n + 8m$ $l = \dfrac{ 20n + 8m }{ -{9} }$ Swap signs so the denominator isn't negative. $l = \dfrac{ -{20}n - {8}m }{ {9} }$